Question

can someone check my answer
What is the solution to the rational equation
x/(x^2-9)+1/(x+3)=1/(4x-12)
I got -9/7 for my answer am i correct???

Answer 1

@Angels

Answer 2

x= 15/7 that wut i got

Answer 3

thanks that was my second choice

Answer 4

ur welcome

Answer 5

\[ \frac{x}{x^2-9} + \frac{1}{x+3} = \frac{1}{4x-12} \]
it looks like you should factor things,
\[ \frac{x}{(x-3)(x+3)} + \frac{1}{x+3} = \frac{1}{4(x-3)} \]

we could find a common denominator, or we could multiply to "clear the denominators"
for example, if we multiply by the common denominator 4(x-3)(x+3) we get

\[ \frac{4x(x-3)(x+3)}{(x-3)(x+3)} + \frac{4(x-3)(x+3)}{x+3} = \frac{4(x-3)(x+3)}{4(x-3)} \\
\frac{4x\cancel{(x-3)(x+3)}}{\cancel{(x-3)(x+3)}} + \frac{4(x-3)\cancel{(x+3)}}{\cancel{(x+3)}} = \frac{\cancel{4(x-3)}(x+3)}{\cancel{4(x-3)}}
\]
that turns into
\[ 4x + 4(x-3) = x+3\\ 4x+4x-12 = x+3\\ 7x= 15\\x= \frac{15}{7}\]